I would disagree with Lieberman in 2000. Unfortunately, there were quite a few southern Dems who didn't like the idea of a Jewish candidate being that close to the White House.
Well what you say may have had an effect, I think there are three main reasons why Lieberman had a substantial negative impact on Gore and cost him the election:
1) Character
When the choice was announced, the media made a big deal about Lieberman having high moral character and that he who would bring “gravitas” to the ticket. Three problems with this:
a. For some of us, it seemed hollow. For example, I may be a crazy liberal, but I take marriage very seriously. Back in the 80s, Lieberman had left his first wife and promptly remarried. What’s so morally upstanding about that?
b. Part of the reason the media used the morality/gravitas narrative is that Lieberman had come out strongly in condemnation of Clinton during the Lewinsky scandal. Thus by picking Lieberman, the campaign spotlight would focus on the “character” aspects of the Clinton years and not so much on the policy aspects. This played right into the hands of the Republicans.
c. If Lieberman was said to bring character and gravitas to the ticket, it implied that these traits were needed. As such, the pick undercut Gore. He was already fighting off attacks on his manliness and honesty. Picking Lieberman was like saying his attackers had a point.
2) Ideology
Whether Gore would be a progressive or a conservative democrat was an issue at the time. Ralph Nader was going on and on with a message that there really wasn’t much difference between the Democrats and the Republicans since both were beholden to corporate special interests. Picking Lieberman made Nader look correct, since many of us view Lieberman as a conservative, hawkish, corporate tool. I believe that some of the 90,000 who voted Nader in Florida did so because of this factor. Remember, that if Gore had won over a little less than 1% of those voters he would have been president.
3) Campaigning
Lieberman was a weak campaigner. His speeches were tepid, his debate was poor and his decision to stay in the Senate race made it look like he didn’t really want to win the VP.